Symmetry And Economic Invariance
Symmetry And Economic Invariance
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DOI：
10.1007/978-4-431-54430-2
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发表时间：
1997-11
期刊：
影响因子：
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通讯作者：
R. Sato;R. Ramachandran
中科院分区：
文献类型：
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作者：
R. Sato;R. Ramachandran
本书介绍了群论的应用，一种数学工具，以检查经济模型的结构。即使对于那些可以用现在经济学中的标准数学方法来分析的模型，群论也提供了更好的直觉。描述动力学模型平衡路径的复杂条件可以用一个简单的守恒定律来表示。反映最近的发展和经济学家之间的兴趣扩大，这个新的增强版有两个部分。第一部分转载了1998年版《对称性与经济不变性》中的章节，第二部分由四章（第8-11章）和一个数学附录（第12章）组成。附录补充了第一章中的数学技巧概述。我们第一次见到对称是在毕达哥拉斯的哲学中，他用对称来赋予一些数字和几何图形以神话般的属性。相反，20世纪的物理学家在分析哲学的影响下，用它来消除经典物理学中没有可观察结果的概念！Sophus Lie展示了如何使用连续群来确定微分方程的可积性，而他的同时代人Felix Klein则使用离散群来编纂欧几里德和非欧几里德几何。今天的数学家将群论与微分拓扑联系起来，同时发展了几何方法，为分析结果提供了直观的解释。我们在经济学中采用了图解分析;我们提供的解释与我们科学中现在流行的实证主义传统是一致的。第1章提供了一个启发式的介绍群论。基本的数学技术介绍和使用群论来确定对称不变性的经济模型进行解释。第二章运用群论分析了生产率增长能否分解为技术进步和规模经济的争论。我们认为，继佐藤（1981），某些类型的技术进步是无法区分的规模经济所产生的特定类型的生产函数。在这个过程中，我们开发了群论中的其他分析概念。v
This book provides an introduction to the application of group theory, a mathematical tool, to examine the structure of economic models. Even for models that can be analyzed by mathematical methods now standard in economics, group theory provides better intuition. Complex conditions that characterize the equilibrium path of a dynamic model can be expressed as a simple conservation law. Reflecting recent developments and a broadening interest among economists, this new enhanced edition has two parts. The first part reproduces the chapters from the 1998 edition of Symmetry and Economic Invariance and the second consists of four chapters (Chapters 8–11) and a mathematical appendix (Chapter 12). The appendix supplements a survey of mathematical techniques in Chapter 1. We first met symmetry in the philosophy of Pythagoras, who used it to attribute mythical properties to some numbers and geometric figures. In contrast, the twentieth-century physicists under the influence of analytical philosophy used it to expunge classical physics of concepts that have no observable consequences! Sophus Lie showed how continuous groups can be used to determine the integrability of differential equations while his contemporary Felix Klein used discrete groups to codify Euclidean and non-Euclidean geometries. Today mathematicians relate group theory to differential topologies while simultaneously developing geometric methods that provide visual interpretation of analytical results. We have adopted in diagrammatic analysis in economics; the interpretations we provide are consistent with the positivist traditions now prevalent in our science. Chapter 1 provides a heuristic introduction to group theory. Basic mathematical techniques are introduced and the use of group theory to determine the symmetric invariance of economic models is explained. Chapter 2 uses group theory to analyze the controversy over whether productivity growth can be decomposed into that arising from technical progress and that from scale economies. We argue, following Sato (1981), that certain types of technical progress are indistinguishable from scale economies generated by particular types of production functions. In the process we develop additional analytical concepts in group theory. v